Asymptotic distribution of the Kaplan-Meier \(U\)-statistics. (English) Zbl 1051.62016
Summary: Consider the Kaplan-Meier estimate of the distribution function for right randomly censored data. We show that a \(U\)-statistic defined via this estimate is asymptotically normal. Under a condition of degeneracy, different from the degeneracy condition in uncensored models, it has an asymptotic nonnormal distribution.
MSC:
| 62E20 | Asymptotic distribution theory in statistics |
| 62N01 | Censored data models |
| 62N02 | Estimation in survival analysis and censored data |
| 62G20 | Asymptotic properties of nonparametric inference |
Keywords:
random censoring; Kaplan-Meier integral; U-statistics; central limit theorem; law of iterated logarithm; degenerate U-statistics; double Wiener integralReferences:
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